The three-dimensional quasi-steady vortex flow field around circular piers in a quasi-equilibrium scour hole under a clear water regime has been investigated experimentally. The main characteristic features of the flow, to be modeled, are a relatively large secondary vortex flow within the scour hole and skewed velocity distributions along the circumference of the pier. The flow field has been divided into a number of parts according to the flow characteristics. The components of quasi-steady velocity for different parts have been theoretically expressed in the form of equations satisfying the continuity equation and the requirements of fitting an individual profile of the measured velocity components. Using the suitable functions, the equations of the velocity components derived for different parts have been combined and matched at the junctions of these parts to get a single equation for each velocity component. The measured data have been utilized to determine the coefficients and exponents used in these equations through curve fittings. The proposed flow model, which corresponds closely with the observations, can be utilized to simulate the flow field in prototype. © ASCE.